A Study of Positive Exponential Consensus on DeGroot Model

A nonlinear consensus model is assigned to resolve the consensus problem of multi-agent systems (MAS). Other studies have constructed consensus systems based on low-complexity computation linear equations or complex nonlinear equations. Linear equations are less efficient in reaching a consensus due to their slow computation process, where nonlinear equations are more efficient. The three major challenges in designing nonlinear consensus equations are: building a system of nonlinear equations that have solution, easy to calculate, and less time consuming. This study aims to create a consensus system that is nonlinear and easy to calculate. According to our survey, the DeGroot model (DGM) of 1974 is a linear model and the first effect consensus model with a flexible computation process for finite nodes. We examine if raising the exponential level for the initial cases of agents allows the system to achieve a consensus and move the DGM to a nonlinear level. The results show that by raising the exponent, the DGM is able to reach a consensus. The consensus of the DGM reaches a certain positive value that depends on the initial states of the agents and the transition matrix, whereas the consensus of the proposed exponential DGM (EDGM) reaches zero with a flexible and unrestricted matrix. Moreover, EDGM is a nonlinear model and reaches the consensus faster than the DGM linear model. The results are supported by theoretical evidence and numerical analysis.